Integral representations of one-dimensional projections for multivariate stable densities

We consider the numerical evaluation of one-dimensional projections of general multivariate stable densities introduced by Abdul-Hamid and Nolan [H. Abdul-Hamid, J.P. Nolan, Multivariate stable densities as functions of one dimensional projections, J. Multivariate Anal. 67 (1998) 80-89]. In their approach higher order derivatives of one-dimensional densities are used, which seems to be cumbersome in practice. Furthermore there are some difficulties for even dimensions. In order to overcome these difficulties we obtain the explicit finite-interval integral representation of one-dimensional projections for all dimensions. For this purpose we utilize the imaginary part of complex integration, whose real part corresponds to the derivative of the one-dimensional inversion formula. We also give summaries on relations between various parametrizations of stable multivariate density and its one-dimensional projection.     

Frequency measurement of pure rotational transitions in the v2 = 1 state of H2O

Frequencies of pure rotational transitions in the v₂ = 1 vibrationally excited state of H₂¹⁶O were measured with a tunable far-infrared spectrometer in the frequency range of 0.5-5 THz. Molecular parameters of Watson’s A-reduced Hamiltonian have been obtained to reproduce the observed frequencies.     

Production of bulk dilute ferromagnetic semiconductor by mechanical milling

We tried to prepare the bulk dilute ferromagnetic semiconductor (DMS) by mechanical milling (MM). Experimental results were as following: (1) The observation of X-ray diffraction and transmitting electron microscopy showed that the particle diameter of host ZnO powder were reduced to about 10 nm by MM. (2) The MM for the mixtures of V₂O₅/ZnO or γ-Fe₂O₃/ZnO realizes the V- or Fe-doped ZnO nano-powders. (3) The values of magnetization under the field of 5 kOe were nearly saturated to 0.8×10⁻³ to 3×10⁻³ μ_B/V-ion for V_xZn_1−xO (x=0.05, 0.1 and 0.2), and 0.2–0.3 μ_B/Fe-ion for Fe_xZn_1−xO (x=0.05 and 0.1) at room temperature. The above results show that the ferromagnetic DMS powder of V_xZn_1−xO and Fe_xZn_1−xO were successfully prepared by MM method.     

STM/STS measurements of two-dimensional electronic states trapped around surface defects in magnetic fields

The local density of states (LDOS) near point defects on a surface of highly oriented pyrolytic graphite (HOPG) was studied at very low temperatures in magnetic fields up to 6 T. We observed localized electronic states over a distance of the magnetic length around the defects in differential tunnel conductance images at the valley energies of the Landau levels (LLs) as well as relatively extended states at the peak ones of LLs. These states appear mainly at energies above the Fermi energy corresponding to the electron LL bands. The data suggest that the quantum Hall state is realized in the quasi two dimensional electron system in HOPG. At the peak energy associated with the n=0 (electron) and -1 (hole) LLs characteristic of the graphite structure, a reduced LDOS around the defects is observed. The spatial distribution is almost field independent, which indicates that it represents the potential shape produced by the defects.     

Theoretical studies on magnetic interactions between Cu(II) ions in salen nucleobases

The magnetic and other physical properties between Cu²⁺ ions coordinated by salen–base pairs (Cu²⁺–DNA) are examined by using DFT calculations. In order to consider effects of entanglement and dis-entanglement of the double helix chain, three types of structural disorders i.e. distance, rotation angle and discrepancy in XY-plane, are changed in the model dimer structure. All calculated results show that J_ab values are weak anti-ferromagnetic couplings. It is also found that the J_ab values strongly depend on the salen structure.     

Multichannel Spectral Imaging System for Measurements with the Highest Signal-to-Noise Ratio

A multichannel spectral imaging system consisting of dichroic mirrors is proposed. The system is expected to have the highest signal-to-noise ratio (SNR) because of the largest optical throughput realized by the multichannel configurations for both imaging and spectrometry. A multichannel spectral imaging system with eight spectral bands was designed by the evolutionary algorithms and then fabricated. The SNR is studied and compared experimentally with those of other fast spectral imaging techniques. A time-sequence of spectral images of a super-continuum light beam is measured using the present system. The number of spectral channels of the system is limited chiefly by the difficulty in designing the arrangement of dichroic mirrors and the optical performance of those mirrors. These limitations restrict the number of spectral channels to approximately 16 at present.     

Conjugate Image Plane Correlator with Holographic Disk Memory

A conjugate image plane correlator with holographic disk memory is proposed. Optical correlation between conjugate images reconstructed from a holographic disk and an input image on liquid-crystal television is executed with the rotation of the disk. Regardless of Fourier hologram recording with the pseudorandom diffuser, it is found possible to take out the diffuser from the original hologram recording scheme using an image reconstruction process and to get correlation signals between input and reconstructed conjugate images in the output plane of a two-lens imaging system. Generation of conjugate replicas with high contrast causes exact matching with an input image which results in high recognition performance for autocorrelation signals. The transfer function of an optical system can be controlled by adjustment of either hologram size or hologram area illuminated with a laser beam. Hence, the output intensity distribution can be adjusted by selecting a proper pupil function and the size of an output pupil defined by the input pupil size and the optical system magnification factor. The real-time character recognition by optical parallel high-speed processing for two dimensional images with position normalization is demonstrated.